It is well recognized that different individuals respond in different ways to the same treatment, and inherited genetic factors play a role on these inter-individual differences. Such genetic factors, referred to as predictive genetic factors, are beginning to enable physicians to make informed therapeutic decisions by tailoring treatments and interventions according to the genetic pro?les of patients. When there is an interaction between a genetic factor and treatment or intervention, it means that treatment bene?ts vary according to the level of the genetic factor. Therefore, epidemiology studies increasingly try to investigate gene-treatment, gene-exposure, and gene-gene interactions in statistical models to identify promising predictive genetic factors. Despite remark- able progress in the identi?cation of etiologic risk factors for cancer, the success rate of identifying interactions and predictive genetic factors remains low. While sample size limitations may partly contribute to this challenge, some signi?cant interactions cannot be replicated because they may be biologically implausible. Therefore, improving the power to detect interactions and developing methodologies to identify practically interpretable interactions and predictive genetic factors are among the critical needs of the ?eld. While there is a large and growing body of work on evaluating interactions for binary outcomes, other richer data types are also be- coming available, and analytic methods to evaluate predictive genetic factors are urgently needed for these settings. The overarching objective of our proposal is to develop formal statistical and mathematical foundations to address these needs. In this R01 project, we propose to show that interactions arising in statistical models corresponding to quantitative expressions for carcinogenesis can be written in a parsimonious manner that can provide insights into the rate at which disease outcome increases in relation to the risk factors. We propose to develop innovative and powerful frequentist and Bayesian statistical techniques to evaluate interactions by harnessing the signi?cant potential of model parsimony. We propose to use these powerful methods to develop well-calibrated models to identify clinically interpretable predictive genetic factors. We also propose to develop and disseminate R libraries that implement our proposed methods. We focus on developing methodologies for count outcomes (measured at a single time point and at two time points) and multiple continuous outcomes measured at a single time point. We will apply our proposed methods to data from three collaborative studies - the study of nevi in children, and cognitive studies of brain and breast cancer patients - and con?rm our results using validation data sets.